A group is said to be pass-alive if it is impossible to capture even if the defender passes regardless of where and how often the attacker plays.
A pass-alive group is alive, but not every live group is pass-alive. Another way to define pass-alive is to say that the status of the group is alive and that no sequence of moves by the attacker only can change this.
There are no ko threats against a group that is pass-alive, not even ``n``-th level ko threats. On the hand, if a group is alive but not pass-alive, there is, for some value of ``n``, an ``n``-th level ko threat against it.
This group, although it is currently alive, is not pass-alive: If Black keeps passing, the group can be captured by White — after White plays at b and then at c it is dead; afterwards, moves at a and d will capture the group.
This group is not pass-alive; a is a 4th level threat to play the 3rd level threat b to play the 2nd level threat c to play the simple (son-ko) threat d.
- Consider a string of a player in a position. The string is pass-alive if for the hypothetical-strategy of the player that consists of only passes the opponent does not have any hypothetical-sequence that starts from the position, with the opponent, and has a capture of the string.
Note: This definition presumes some other definitions for the terms used therein.